On his blog, Mohler explains that he came to this conviction after reading The Subtle Body by Stefanie Syman:
Syman describes yoga as a varied practice, but she makes clear that yoga cannot be fully extricated from its spiritual roots in Hinduism and Buddhism. She is also straightforward in explaining the role of sexual energy in virtually all forms of yoga and of ritualized sex in some yoga traditions. She also explains that yoga “is one of the first and most successful products of globalization, and it has augured a truly post-Christian, spiritually polyglot country.”
Can Yoga exercises be separated from Eastern religion? They already are in American culture. You can visit people in shopping malls who teach yoga that don't know the first thing about Eastern ideas of religion or meditation. Yoga is certainly a strong religion, but the exercises that it brought to us have already been taken out of their religious context, and no one is forsaking their own religion when they stretch their calves and breath deeply.
Concerning sexual energy, there's nothing wrong with that. In fact, the married people I know (myself included) are thankful that humans have sexual energy. And the fact that Syman documents ritualized sex has nothing to do with an individual stretching out on a mat in their own home (unless those Yoga videos are more edgy then I think they are). And it misrepresents Yoga, frankly; it's not good to malign every Yoga teacher by casting them as a pervert.
Finally, there's an argument in there about globalization. It is really hip to hate globalization, but it doesn't really do anything for this conversation. Yes, the globalizing of cultures brought Yoga to America. But casting stones at globalization isn't helpful to a discussion about Yoga, unless the author thinks that cultures need to stop learning about each other. There's nothing wrong with globalization.
Is America a post-Christian country? Yes. Is Yoga responsible? No. The seeds of post-Christianity were planted long before Yoga was introduced to the Western world, and without Yoga we would be in the same place, religiously. The roots of post-Christianity go much deeper than any single religious movement.
So, in conclusion, don't throw away your Yoga mat. You're not embracing another religion when you perform Yoga exercises any more than I embrace Charles Manson when I listen to the White Album. Sure, these workouts came from a set of religious practices, but in America Yoga is mostly known for its fitness appeal and is only linked to religion by an individual's choice. Keep stretching.